Let $\mathbb{R}$ denote the set of all real numbers and let $i=\sqrt{-1}$. Consider the matrices

$$ S=\left[\begin{array}{rr} 0 & -1 \\ 1 & 0 \end{array}\right] \quad \text { and } \quad T=\left[\begin{array}{ll} 1 & 1 \\ 0 & 1 \end{array}\right] . $$

Let $a, b, c, d$ be real numbers such that

$$ S T=\left[\begin{array}{ll} a & b \\ c & d \end{array}\right] $$

Let

$$ H=\{x+i y: \quad x, y \in \mathbb{R} \text { and } y>0\} . $$

Then which of the following statements is (are) TRUE ?

Let ℝ denote the set of all real numbers. Let $z_1 = 1 + 2i$ and $z_2 = 3i$ be two complex numbers, where $i = \sqrt{-1}$. Let

$$S = \{(x, y) \in \mathbb{R} \times \mathbb{R} : |x + iy - z_1| = 2|x + iy - z_2| \}.$$

Then which of the following statements is (are) TRUE?